Chapter 10, Problem 25SE

Violins Professional musicians listened to five violins being played, without seeing the instruments. One violin was a Stradivarius, and the other four were modern-day violins. When asked to pick the Stradivarius (after listening to all five), 39 got it right and 113 got it wrong.

a. Use the chi-square goodness-of-fit test to test the hypothesis that the experts are not simply guessing. Use a significance level of $0.05$.

b. Perform a one-proportion $z\text{-test}$ with the same data, using a one-tailed alternative that the experts should get more than $20\%$ correct. Use a significance level of $0.05$.

c. Compare your $\text{p-values}$ and conclusions.